The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  1  1
 0  X  0  0  0  0  0  0 X^2 X^2  X X^2+X  X X^2+X  X  X X^2 X^2 X^2  X  0  X X^2  X X^2+X X^2+X X^2  X  X  0 X^2 X^2
 0  0  X  0  0  0  0  0  0  0  0  0 X^2  X  X X^2+X X^2+X  X  X  X  X X^2 X^2 X^2+X X^2  X  X  0 X^2+X  X X^2  0
 0  0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2  0  X X^2+X X^2+X X^2  0 X^2  X  X X^2+X X^2  0  0 X^2+X X^2+X  0 X^2 X^2  0
 0  0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0 X^2 X^2+X  0  0 X^2+X X^2+X  X X^2+X  0  X X^2  X  0 X^2 X^2 X^2  0  X  X
 0  0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  X  X  X X^2+X  X X^2+X  0  X  X X^2+X X^2 X^2 X^2 X^2+X  0  0  0 X^2+X  0  0

generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+74x^24+116x^25+176x^26+250x^27+286x^28+346x^29+704x^30+1322x^31+1603x^32+1346x^33+734x^34+382x^35+272x^36+222x^37+168x^38+94x^39+66x^40+18x^41+9x^42+2x^44+1x^58

The gray image is a linear code over GF(2) with n=128, k=13 and d=48.
This code was found by Heurico 1.16 in 2.07 seconds.